State-of-the-art legged robots are either capableof measuring torque at the output of their drive systems, orhave transparent drive systems which enable the computationof joint torques from motor currents. In either case, this sensormodality is seldom used in state estimation. In this paper,we propose to use joint torque measurements to estimate thecentroidal states of legged robots. To do so, we project thewhole-body dynamics of a legged robot into the nullspace ofthe contact constraints, allowing expression of the dynamics independent of the contact forces. Using the constrained dynamicsand the centroidal momentum matrix, we are able to directlyrelate joint torques and centroidal states dynamics. Using theresulting model as the process model of an Extended KalmanFilter (EKF), we fuse the torque measurement in the centroidalstate estimation problem. Through real-world experiments ona quadruped robot executing different gaits, we demonstratethat the estimated centroidal states from our torque-based EKFdrastically improve the recovery of these quantities comparedto direct computation.